Hodgkin-Huxley Model Indicates an Inversion in the Strength-Duration Curves for Mono and Biphasic Stimuli

Abstract

Action potentials are non-linear variations of the transmembrane potential caused by changes in the membrane conductance. In 1952, Hodgkin and Huxley proposed a set of differential equations that describes mathematically the conductance changes observed during the course of an action potential. Currently, this model is still a good tool for understanding the basic mechanisms involved in the initiation and propagation of the action potentials. The objective of this work was to use a simple application of the Hodgkin-Huxley model to define the relation between the stimulation threshold and variations of the stimulatory waveform, in order to promote cell excitation delivering the lowest energy stimulus. We evaluated the strength-duration curves for mono and biphasic stimuli, giving special attention to short stimuli. This Hodgkin-Huxley implementation allowed the explanation of the mechanisms underlining a curious inversion of the strength-duration curves for mono and biphasic stimuli. Namely, for shorter stimuli (<2.2 ms), the stimulation threshold for monophasic stimuli becomes smaller than for biphasic stimuli. That inversion seems to be a result of the time-dependence of the activation variables of Na⁺ and K⁺ channels and the inactivation variable of Na⁺ channels proposed in the Hodgkin-Huxley model. In addition, we used the model to evaluate the energy of asymmetrical biphasic stimuli in order to find a more energy-efficient waveform, which was shown to be a combination of a 7 ms long hyperpolarizing phase with a depolarizing phase of 6 ms.